Problem: Simplify the following expression: $ r = \dfrac{-n - 5}{n + 1} - \dfrac{-7}{5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-n - 5}{n + 1} \times \dfrac{5}{5} = \dfrac{-5n - 25}{5n + 5} $ Multiply the second expression by $\dfrac{n + 1}{n + 1}$ $ \dfrac{-7}{5} \times \dfrac{n + 1}{n + 1} = \dfrac{-7n - 7}{5n + 5} $ Therefore $ r = \dfrac{-5n - 25}{5n + 5} - \dfrac{-7n - 7}{5n + 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-5n - 25 - (-7n - 7) }{5n + 5} $ Distribute the negative sign: $r = \dfrac{-5n - 25 + 7n + 7}{5n + 5}$ $r = \dfrac{2n - 18}{5n + 5}$